Dr. Aaron Titus | Department of Physics, High Point University
PHY1050      Astronomy of Stars, Galaxies, and the Cosmos
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part 1

Two consecutive peaks of a wave are called a cycle. The distance between peaks is called wavelength. The time it takes for two consecutive peaks to pass a certain point is called period. The number of cycles to pass a certain point in one second is called frequency.

In the simulation below, there are four animations, called Wave 1, Wave 2, Wave 3, and Wave 4, each showing a different wave. We are going to measure both wavelength and frequency for the four waves.

For this activity, make a table, like the one below, in a spreadsheet or on a separate piece of paper. This is where you will record observations and measurements.

Wave Observation Wavelength (m) Frequency (Hz)
Wave 1      
Wave 2      
Wave 3      
Wave 4      

Click the link for each wave (links are below the animation) and compare what you see. Write your observation in the table.

You probably noticed that the first animation shows the longest (or largest) wavelength, and the fourth animation shows the shortest (or smallest) wavelength.

Measure the wavelength of each wave. To do this, click and hold your mouse at at wave crest (highest point of a wave). The coordinate shown are x (horizontal) and y (vertical) coordinates of this wave crest. Record the x-value. Now click and hold your mouse at the next wave crest to the right of the one you just measured. Record the x-coordinate of this crest. Calculate the difference in these values. This is the x (or horizontal) distance between successive wave crests which is the wavelength of the wave.

Measure and record the wavelength of each wave. Let's assume that units are meters.

Now, for each case, you will measure the number of wave crests (or cycles) that pass the mark in one second. (Don't count the first crest at time t=0). I will describe what to do for the first wave.

Clink the link Show Wave 1 to view the first animation. Note the blue marker. Let's count how many peaks reach the blue marker in one second. We do not count the first peak that is at the blue marker at t=0. Click the "Step >>" button to step forward at tenth of a second intervals. Continue doing this until t=1 s. Count how many peaks reach or pass the blue marker between t=0 and t=1 s. So, how many peaks per second passed the blue marker?

Now, measure the frequency in Hz (hertz) of each of the other waves--Wave 2, Wave 3, and Wave 4--by clicking those links. Check the answers by clicking the buttons below.

Record your results for the frequency of the four waves in the data table.

Now this is the fun part! Examine your measurements for wavelength and frequency. As you look at the numbers for the wavelength from wave 1 to wave 4, you will notice that the wavelength is smaller from wave 1 to wave 4. But as the wavelength gets smaller, what happens to the frequency?

We call this type of relationship an inverse relationship. Wavelength and frequency are inversely proportional. Thus:

A wave with a large wavelength has a small frequency.

And a wave with a small wavelength has a large frequency.

There's something else that you might notice in the data. What is the product of wavelength x frequency for each wave? (Add a new column and compute this value for each wave.)

Just as the speed of each of these waves is the same, the speed of different wavelength (and frequency) light waves in a vacuum (space) is the same. In this animation, you calculated the speed of these waves to be 3 m/s. However, the speed of light in a vacuum is actually 300,000,000 m/s!

You've just discovered the equation: wavelength x frequency = speed of light. COOL!






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